I'm afraid this might not really prove anything.
If two different strategies were designed to meet different objectives,
then it is inherently meaningless to compare them by a _single_
standard, because any single standard will be biased toward one
objective or the other.
Example: Most royals or most dollars?
Strategy R is designed to maximizes the player's probability
of surviving long enough to hit a royal flush. After hitting one royal
flush, the player may choose to quit or may choose to continue
playing for another royal.
Strategy G is designed to maximizes the player's growth rate,
similar to Kelly play. The player intends to change unit size
as his/her bankroll grows/shrinks in order to keep bets as
close to log-optimal as possible.
Now let's set up a comparison by starting two players with
100 units and having them each play for "long enough"
but both play the same coin in, in order to compare these
two strategies. This might seem like a fair comparison, but
it is biased in favor of strategy G. The probability of G
winning the contest will tend to increase as we increase
the amount of coin-in used for the comparison.
If we start each player with 100 units and let them each
play until they either go broke or hit a royal flush, then
strategy R will prevail, since this is a direct measure
of the objective that strategy R was designed to achieve.
Bias toward strategy R.
In is fundamentally impossible to design an exeriment
that is "universally unbiased" in nature. Any procedure
that purports to compare performance is equivalent to
defining an objective or goal (call it X) and measuring
performance by the standards of goal X. There will be
some other strategy that optimizes X. When we now
try to compare strategies R and G using this new
experiment, we are really determing which of the two
is closest to "the strategy which optimizes X."
RS can simply claim that his strategy "wins his way"
whatever that means. Unless he can be pinned down
to define that in a way which is mathematically precise,
it may be impossible to prove or disprove that his
recommendations actually match up with a strategy that
achieves the stated objectives. True optimization is
a difficult process, and using a seat-of-the-pants
approach to design an "optimal" strategy is extremely
unlikely to result in a correct solution. When it comes
to gambling, intuition and hunches just tend to suck.
ยทยทยท
On Saturday 17 April 2004 06:25 am, TedChee@aol.com wrote:
Was just thinking wouldn't it be interesting to have a challenge?
One of the major authors & RS in a playoff. To accommodate RS's
game-switching & hit & run style, both would play the same coin-in, switch
denominations at the same coin-in & quit at the same coin-in. Both would be
free to play whatever VP they wanted. Probably need a minimum coin-in per
session & unbiased auditors.
Run it over 10 sessions in 10 casinos.
Loser pays winner 2X the difference in their final win/loss.